The correct answer is 1. The Public Service Commission, which is the original version of the U.P.S.C. (Union Public Service Commission), was set up on 1st October, 1926. It was established to oversee the recruitment and selection process for civil service positions in India.

Option 2, 1st April, 1937, is incorrect.

Option 3, 15th August, 1947, is incorrect as this date signifies India`s independence from British rule and not the establishment of the Public Service Commission.

Option 4, 26th January, 1950, is incorrect as this date marks the adoption of the Constitution of India and the official establishment of the Republic of India.

It is important to note that the U.P.S.C. as we know it today was formed in 1950 after the adoption of the Constitution.